# kVA, kW and Power Factor Calculator

> Completes the AC power triangle from any two of apparent power (kVA), real power (kW), reactive power (kVAR) and power factor, reports the phase angle and, when a voltage is given, the single- or three-phase line current, plus the capacitor kVAR needed to correct the power factor to 0.95.

- Calculator id: `kva-kw-power-factor` · Category: Engineering & Automotive (`engineering`) · Tool name: `convert_kva_kw_power_factor`
- Canonical page: https://tttkmbb.com/engineering/kva-kw-power-factor · This document: https://tttkmbb.com/engineering/kva-kw-power-factor.md · JSON definition: https://tttkmbb.com/engineering/kva-kw-power-factor.json

## Purpose

Completes the AC power triangle from any two of apparent power (kVA), real power (kW), reactive power (kVAR) and power factor, reports the phase angle and, when a voltage is given, the single- or three-phase line current, plus the capacitor kVAR needed to correct the power factor to 0.95.

**Use when:** You need to convert a transformer, generator or UPS kVA rating to usable kW, find the power factor or reactive power of a load, size a power-factor-correction capacitor bank, or get the current for a kVA load at a voltage.

**Do not use when:** You have line voltage and current of a balanced three-phase load and want the full per-phase breakdown (use three-phase-power), or the load is DC or non-sinusoidal with strong harmonics (displacement and distortion power factor differ).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `apparent_power_kva` | number | kVA | optional | Apparent power in kilovolt-amperes (the nameplate rating of transformers and generators). (> 0, max 10000000) |
| `real_power_kw` | number | kW | optional | Real (active) power in kilowatts, the part that does work and is billed as energy. (min 0, max 10000000) |
| `power_factor` | number |  | optional | cos φ between 0 and 1 (typical: motors 0.8–0.9, resistive heaters 1.0). (> 0, max 1) |
| `reactive_power_kvar` | number | kVAR | optional | Reactive power in kilovolt-amperes reactive (magnetising power of motors and transformers). (min 0, max 10000000) |
| `voltage_v` | number | V | optional | Optional RMS supply voltage (line-to-line for three-phase); enables the current output. (> 0, max 1000000) |
| `phases` | enum: single \| three |  | optional, default "three" | Supply type used for the current calculation. |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `apparent_power_kva` | number | kVA | S = √(P² + Q²) = P / PF. |
| `real_power_kw` | number | kW | P = S × PF. |
| `reactive_power_kvar` | number | kVAR | Q = √(S² − P²). |
| `power_factor` | number |  | PF = P / S = cos φ. |
| `phase_angle_degrees` | number | ° | φ = arccos(PF), the angle between voltage and current. |
| `current_a` | number | A | I = S × 1000 / V (single-phase) or S × 1000 / (√3 × V) (three-phase); only when voltage_v is given. |
| `kvar_to_reach_pf_0_95` | number | kVAR | Reactive compensation needed to raise the power factor to 0.95: Q − P × tan(arccos 0.95); 0 when PF is already 0.95 or higher. |
| `pf_correction_note` | string |  | Plain-language note on correcting the power factor to the common 0.95 target (lagging load assumed). |
| `given` | string |  | Which two inputs the triangle was solved from. |

## Formula

`S² = P² + Q²; PF = P / S; φ = arccos(PF); from S and PF: P = S × PF, Q = √(S² − P²); from P and Q: S = √(P² + Q²); from P and PF: S = P / PF; from PF and Q: S = Q / √(1 − PF²); current_a = S × 1000 / voltage_v (single) or S × 1000 / (√3 × voltage_v) (three); kvar_to_reach_pf_0_95 = max(0, Q − P × tan(arccos 0.95))`

Power-triangle relations for sinusoidal AC (displacement power factor). The load is assumed inductive (lagging), which is the usual case for motors and transformers; a leading (capacitive) load has the same magnitudes with the opposite sign of Q.

## Data Sources

- Wikipedia – AC power (power triangle) — https://en.wikipedia.org/wiki/AC_power (reference, retrieved 2026-09-24)
- Wikipedia – Power factor — https://en.wikipedia.org/wiki/Power_factor (reference, retrieved 2026-09-24)

Data freshness: `static`. Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output.

## API

- `GET https://tttkmbb.com/api/v1/calculate/kva-kw-power-factor?`
- `POST https://tttkmbb.com/api/v1/calculate/kva-kw-power-factor` with JSON body `{"inputs": {…}}`
- Response: unified envelope (`success`, `request`, `result.values`, `result.units`, `sources`, `freshness`, `timestamp`, `next_actions`, `links`); see https://tttkmbb.com/docs/response-format.md
- Schema: https://tttkmbb.com/api/v1/calculators/kva-kw-power-factor · OpenAPI operationId `convert_kva_kw_power_factor` in https://tttkmbb.com/openapi.json
- Authentication: none. Rate limit: fair use, see https://tttkmbb.com/docs/rate-limits.md.

## MCP

- Server: `https://tttkmbb.com/mcp` (Streamable HTTP, JSON-RPC 2.0, no auth)
- Tool:  `run_calculator` with `{"calculator_id": "kva-kw-power-factor", "inputs": {…}}`

## Example

- 100 kVA at PF 0.8, 400 V three-phase: inputs `{"apparent_power_kva":100,"power_factor":0.8,"voltage_v":400,"phases":"three"}` → `{"apparent_power_kva":100,"real_power_kw":80,"reactive_power_kvar":60,"power_factor":0.8,"phase_angle_degrees":36.87,"current_a":144.338,"kvar_to_reach_pf_0_95":33.705}`
- 50 kW and 30 kVAR: inputs `{"real_power_kw":50,"reactive_power_kvar":30}` → `{"apparent_power_kva":58.31,"power_factor":0.8575,"phase_angle_degrees":30.96,"kvar_to_reach_pf_0_95":13.566}`

```
GET https://tttkmbb.com/api/v1/calculate/kva-kw-power-factor?apparent_power_kva=100&power_factor=0.8&voltage_v=400&phases=three
```

## Limitations

You have line voltage and current of a balanced three-phase load and want the full per-phase breakdown (use three-phase-power), or the load is DC or non-sinusoidal with strong harmonics (displacement and distortion power factor differ). Power-triangle relations for sinusoidal AC (displacement power factor). The load is assumed inductive (lagging), which is the usual case for motors and transformers; a leading (capacitive) load has the same magnitudes with the opposite sign of Q. All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**Why is kVA larger than kW?**

Real power is only the component of the apparent power in phase with the voltage; the remaining reactive power circulates between source and load without doing work but still loads conductors and transformers. kW = kVA only at power factor 1.

**How much capacitor kVAR do I need for correction?**

The load's reactive power minus the reactive power allowed at the target factor: Q_c = P × (tan φ₁ − tan φ₂). For 80 kW at PF 0.8 corrected to 0.95 that is 60 − 26.3 ≈ 33.7 kVAR.

**Why can I not enter PF 1 with a reactive power?**

At unity power factor the reactive power is zero by definition, so the pair is contradictory; give real or apparent power instead.

## Related

- [Three-Phase Power Calculator](https://tttkmbb.com/engineering/three-phase-power.md) — Full per-phase breakdown for balanced three-phase loads.
- [Electric Power Calculator](https://tttkmbb.com/physics/electric-power.md) — P = V × I for DC and unity power factor.
- [Wire Voltage Drop Calculator](https://tttkmbb.com/engineering/wire-voltage-drop.md) — Cable drop for the resulting current.